Today’s comic strip features Venn diagrams:
Ruthie wants to know who this Venn person is, and whether she can get money for a invention called “the ruthie diagram” which uses squares instead of circles.
Lots of interesting stuff here that we might pursue at length. One is the whole domain of the history of mathematics: who are the people that came up with these crazy ideas, and what was the intellectual/problem environment in which their ideas made sense? In math class we rarely spend much time looking at the history of mathematical ideas; and if we do, we tend to give little homilies instead, like the one about Einstein being a poor student in high school. The history of ideas tends to get short shrift, whether in math class or in history class. (Interestingly, in another sense, a very large part of the math curriculum implicitly represents the frozen history of math ideas but in a way that is unexamined.)
Two, there is the whole domain of attribution. An idea gets named after somebody, and we learn the idea together with the name. How does this attribution work? An interesting example of this, for me, is with Mendel’s laws. This is not an example in mathematics as such, but in heredity and inheritance of traits. The story I learned way back in high school is that Mendel was this monk who did his work in total obscurity for years, until he got some great results. I had never seen an update of that story during my own later studies, but got curious about how a monk at an obscure monastery was able to get his results published and seen by the relevant people in the field. Well, it turns out he kind of didn’t. The update to the story I learned later is that Mendel’s work did not get seen by the relevant people in the field. Mendel was either uninterested, or incompetent, or unlucky, in the matter of getting his results seen by the right people. I’m not even sure his papers got published at all. Somebody else published results, independently rediscovered, and it was those published results that moved the field forward. Later, it was discovered that Mendel’s unknown work had predated it. So now we associate Mendel with the discovery, though Mendel was not a clear link in the chain of discoveries that moved the understanding of heredity forward. Apparently, the laws of attribution are mostly about dates of notes in notebooks and not about the flow of ideas and intellectual conversation. Yet, once attributed to somebody, there is a certain inertia in changing it, even in the face of later clear evidence. You can imagine that if we were to find a Chinese manuscript with a clear statement and proof of the Pythagorean law yet predating Pythagoras by many centuries, we still might not update all those textbooks immediately if at all.
Coming back to attribution and Venn diagrams, this Wiki entry acknowledges that the use of diagrams popularized by John Venn through his 1880 paper did originate much earlier. The Wiki entry also claims that Venn didn’t call them Venn diagrams, they weren’t called Venn diagrams until Clarence Irving Lewis called them that in 1918.
Three, there is the whole domain of money and ideas. Attribution and money don’t seem to have much to do with each other. If Pythagoras got a dime each time his name was mentioned in relationship to triangles, his heirs might be rich. Yet that isn’t how it works. Money flow is important, but it isn’t the only thing of importance. The vast flow of ideas that had to come to fruition across the ages that eventually resulted in my $3 calculator – what a great gift to me, simply for being born in this age and in this society.
Update 2009/03/08: A wikipedia article about Hugo de Vries mentions that Mendel did publish his paper. Hugo de Vries published results in 1889 in a book Intracellular Pangenesis, and found Mendel’s paper afterwards, in “the late 1890’s”.